The Complexity of Explaining Negative Query Answers in
DL-Lite

Proc. of the 13th Int. Conf. on the Principles of Knowledge
Representation and Reasoning (KR 2012). 2012.

In order to meet usability requirements, most logic-based
applications provide explanation facilities for reasoning services.
This holds also for DLs, where research has focused on the
explanation of both TBox reasoning and, more recently, query
answering. Besides explaining the presence of a tuple in a query
answer, it is important to explain also why a given tuple is
missing. We address the latter problem for (conjunctive) query
answering over DL-Lite ontologies, by adopting abductive reasoning,
that is, we look for additions to the ABox that force a given tuple
to be in the result. As reasoning tasks, we consider existence and
recognition of an explanation, and relevance and necessity of a
certain assertion for an explanation. We characterize the
computational complexity of these problems for subset minimal and
cardinality minimal explanations.